The paper describes the upscaling and reservoir simulation of a giant Middle East oil field, the geological modeling of which is described in a companion paper.1 The main objective of the study was the simulation of the irregular water advance observed in some parts of the field as a consequence of peripheral water injection.

Three scales of heterogeneity were identified in the characterization phase: the matrix, the stratiform Super-K intervals, and the fractures. To accommodate the different hydraulic properties of each heterogeneity system, a dual-media approach (dual porosity and dual permeability) was used.

The assignment of the effective properties to the simulation grids (matrix and fracture grids) was performed independently for the three heterogeneity systems. In particular, the geostatistical facies model was upscaled with algebraic methods, while the stratiform Super-K layers and fracture properties were reproduced explicitly at the simulation gridblock scale through an original upscaling procedure.

The history match was achieved in a short time by a small variation of the fractal dimension of the fracture distribution and without resorting to any local modification.

Simulation results showed that the fracture system was the controlling factor in terms of water advance and breakthrough, while the impact of the stratiform Super-K layers proved to be of second order.

In a later stage, the model was used to run production forecasts under different exploitation scenarios.

The conclusions of this study indicate that for such porous and fractured reservoirs with stratiform Super-K occurrences, a detailed characterization of all the heterogeneity systems, coupled with a dual-media formulation, is necessary for accurate reservoir simulation and effective reservoir management.

Introduction

Heterogeneities are always present, to some degree, in natural petroleum reservoirs.2 Their impact can be very important in the overall dynamic behavior of the reservoirs, especially when secondary recovery projects are active (e.g., water or gas injection).

In the Middle East, many oil reservoirs are currently experiencing unexpected production performance, especially early water breakthrough (BT), which usually starts soon after the implementation of waterflooding projects. In most studies, such unexpected behavior is generically related to the presence of reservoir heterogeneity in the form of some high-permeability conduits that link the injector and producer wells. Note that while such simplified understanding can be sufficient for a history-matching exercise, a much better description of the reservoir heterogeneity is required, in terms of type and distribution, when the simulation model is used in forecasting mode.

This project concentrated on the geological description, upscaling, and numerical simulation of a giant Middle East carbonate reservoir, which experienced early water BT in some parts of the field. Because it was felt that reservoir heterogeneity was the driving factor behind this unexpected behavior, most of the effort was devoted to the description and simulation of such heterogeneity.

The geological characterization of the reservoir is described in a companion paper.1 Three main heterogeneity systems were identified:

1. The matrix. This consists of porous and permeable (up to 200 md) limestones and dolomites. A rock-type classification system was established by means of a multivariate statistical algorithm. Vertical and horizontal proportion curves were generated within a sequence stratigraphy framework, which showed strong nonstationary behavior. Eventually, a 3D facies geostatistical model was generated. Petrophysical properties were assigned to the fine-scale grid through an original inversion algorithm based on flowmeter data.3

2. The stratiform Super-K intervals. These are thin, highly permeable layers with conductivity in excess of 500 B/D/ft. Their permeability is typically on the order of 1 to 5 darcies. Such intervals are defined through the analysis of the available flowmeters, and they have been included in the geostatistical model using a plurigaussian algorithm. A strong relationship between stratigraphic position and stratiform Super-K intervals was demonstrated. The extension, the shape, and the continuity of these bodies are largely unknown and are key factors of the characterization phases.

3. The fractures. The presence of fractures has been inferred through the analysis of data from seismic interpretation, curvature analysis, and wellbore logs. Fractures do cluster in swarms that can be represented as heavily fractured lineaments (called fracture in the following sections). All the available data concerning these fracture swarms were integrated in a stochastic fault and fracture model, and alternative images were generated through a fractal approach.

It should be stressed that the presence of significant fracture patterns has been proposed for the first time in this study because reservoir performances historically have been related mainly to matrix and Super-K characteristics and distribution.4,5

In the next sections, we describe the impact of these reservoir heterogeneities on the field behavior and the implementation of the available geological characterization in the simulation model.

Problem Statement

The field under study is a giant carbonate reservoir that has been on stream for almost 30 years. The reservoir was producing under fluid expansion and weak aquifer drive until 1995, when a waterflooding project started. Fig. 1 shows a map of the reservoir structure. Note that the field is part of a much larger oil accumulation that extends to the south and to the north; therefore, these limits do not correspond to real reservoir boundaries. The inner window shows the area retained for numerical simulation (pilot area).

The main problem of the field under study is early water BT, especially in some wells located in the western flank. Such behavior has been observed in recent years, after the start of the waterinjection project, while no significant water production had been measured before that date.